{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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sfXpb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\nphy+Op7fwL/jxx5Kfzf+uLH2p/xfT/HH/9k=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image \n",
    "Image('../../../python_for_probability_statistics_and_machine_learning.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Support Vector Machines\n",
    "\n",
    "Support Vector Machines (SVM) originated from the statistical learning theory\n",
    "developed by Vapnik-Chervonenkis. As such, it represents a deep application of\n",
    "statistical theory that incorporates the VC dimension concepts we\n",
    "discussed in the first section. Let's start by looking at some pictures.\n",
    "Consider the two-dimensional classification problem shown in\n",
    "[Figure](#fig:svm_001).  [Figure](#fig:svm_001) shows two classes (gray and\n",
    "white\n",
    "circles) that can be separated by any of the lines shown. Specifically, any\n",
    "such separating line can be written as the locus of points ($\\mathbf{x}$) in\n",
    "the two-dimensional plane that satisfy the following,\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/svm_001.png, width=500 frac=0.45] In the\n",
    "two-dimensional plane, the two classes (gray and white circles) are easily\n",
    "separated by any one of the lines shown.   <div id=\"fig:svm_001\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:svm_001\"></div>\n",
    "\n",
    "<p>In the two-dimensional plane, the two classes (gray and white circles) are\n",
    "easily separated by any one of the lines shown.</p>\n",
    "<img src=\"fig-machine_learning/svm_001.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "$$\n",
    "\\beta_0 + \\boldsymbol{\\beta}^T \\mathbf{x} = 0\n",
    "$$\n",
    "\n",
    " To classify  an arbitrary $\\mathbf{x}$ using this line, we just\n",
    "compute the sign of $\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}$ and assign one\n",
    "class to the positive sign and the other class to the negative sign.  To\n",
    "uniquely specify such a separating line (or, hyperplane in a higher-dimensional\n",
    "space) we need additional criteria.\n",
    "\n",
    "\n",
    "[Figure](#fig:svm_002) shows the data with two bordering parallel lines that\n",
    "form a margin around the central separating line.  The *maximal margin\n",
    "algorithm* finds the widest margin and the unique separating line.  As a\n",
    "consequence, the algorithm uncovers the elements in the data that touch the\n",
    "margins. These are the *support* elements. The other elements\n",
    "away from the border are not relevent to the solution. This reduces\n",
    "model variance because the solution is insensitive to the removal of\n",
    "elements other than these supporting elements (usually a small minority).\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/svm_002.png, width=500 frac=0.55] The\n",
    "maximal margin algorithm finds the separating line that maximizes the margin\n",
    "shown. The elements that touch the margins are the support elements. The dotted\n",
    "elements are not relevent to the solution. <div id=\"fig:svm_002\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:svm_002\"></div>\n",
    "\n",
    "<p>The maximal margin algorithm finds the separating line that maximizes the\n",
    "margin shown. The elements that touch the margins are the support elements. The\n",
    "dotted elements are not relevent to the solution.</p>\n",
    "<img src=\"fig-machine_learning/svm_002.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "To see how this works for linearly separable classes, consider a\n",
    "training set consisting of $\\lbrace (\\mathbf{x},y) \\rbrace$ where\n",
    "$y\\in \\lbrace -1,1 \\rbrace$. For any point $\\mathbf{x}_i$, we\n",
    "compute the functional margin as $\\hat{ \\gamma_i }=y_i (\\beta_0 +\n",
    "\\boldsymbol{\\beta}^T \\mathbf{x}_i)$. Thus, $\\hat{\\gamma}_i >0$ when\n",
    "$\\mathbf{x}_i$ is correctly classified. The geometrical margin is\n",
    "$\\gamma = \\hat{\\gamma}/\\lVert\\boldsymbol{\\beta}\\rVert$. When\n",
    "$\\mathbf{x}_i$ is correctly classified, the geometrical margin is\n",
    "equal to the perpendicular distance from $\\mathbf{x}_i$ to the line.\n",
    "Let's look see how the maximal margin algorithm works.\n",
    "\n",
    "Let $M$ be the width of the margin.  The maximal margin algorithm is can be\n",
    "formulated as a quadratic programming problem. We want to simultaneously\n",
    "maximize the margin $M$ while ensuring that all of the data points are\n",
    "correctly classified.\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\underset{\\beta_0,\\boldsymbol{\\beta},\\lVert\\boldsymbol{\\beta}\\rVert=1}{\\text{m\n",
    "aximize}}\n",
    "& & M \\\\\\\n",
    "& \\text{subject to:}\n",
    "& & y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq M, \\; i = 1, \\ldots, N.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    " The first line says we want to generate a maximum value for $M$ by\n",
    "adjusting $\\beta_0$ and $\\boldsymbol{\\beta}$ while keeping\n",
    "$\\lVert\\boldsymbol{\\beta}\\rVert=1$. The functional margins for each $i^{th}$\n",
    "data element are the constraints to the problem and must be satisfied for every\n",
    "proposed solution. In words, the constraints enforce that the elements have to\n",
    "be correctly classified and outside of the margin around the separating line.\n",
    "With some reformulation, it turns out that\n",
    "$M=1/\\lVert\\boldsymbol{\\beta}\\rVert$ and this can be put into the following\n",
    "standard format,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\underset{\\beta_0,\\boldsymbol{\\beta}}{\\text{minimize}}\n",
    "& & \\lVert\\boldsymbol{\\beta}\\rVert \\\\\\\n",
    "& \\text{subject to:}\n",
    "& & y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq 1, \\; i = 1, \\ldots, N.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    " This is a convex optimization problem  and can be solved using\n",
    "powerful\n",
    "methods in that area.\n",
    "\n",
    "The situation becomes more complex when the two classes are not separable and\n",
    "we have to allow some unavoidable mixing between the two classes in the\n",
    "solution. This means that the contraints have to modified as in the following,\n",
    "\n",
    "$$\n",
    "y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq M(1-\\xi_i)\n",
    "$$\n",
    "\n",
    " where the $\\xi_i$ are the slack variables and represent the\n",
    "proportional amount tha the prediction is on the wrong side of the margin. Thus,\n",
    "elements are misclassified when $\\xi_i>1$. With these additional variables,\n",
    "we have a more general formulation of the convex optimization problem,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\underset{\\beta_0,\\boldsymbol{\\beta}}{\\text{minimize}}\n",
    "& & \\lVert\\boldsymbol{\\beta}\\rVert \\\\\\\n",
    "& \\text{subject to:}\n",
    "& & y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq 1-\\xi_i, \\\\\\\n",
    "& & & \\xi_i \\geq 0, \\sum \\xi_i \\leq \\texttt{constant}, \\; i = 1, \\ldots, N.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    " which can be rewritten in the following equivalent form,\n",
    "\n",
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"eq:svm\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "& \\underset{\\beta_0,\\boldsymbol{\\beta}}{\\text{minimize}}\n",
    "& & \\frac{1}{2}\\lVert\\boldsymbol{\\beta}\\rVert + C \\sum \\xi_i \\\\\\\n",
    "& \\text{subject to:}\n",
    "& & y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq 1-\\xi_i, \\xi_i \\geq 0 \\;\n",
    "i = 1, \\ldots, N.\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\\label{eq:svm} \\tag{1}\n",
    "$$\n",
    "\n",
    " Because the $\\xi_i$ terms are all positive, the objective\n",
    "is to maximize the margin (i.e., minimize $\\lVert\\boldsymbol{\\beta}\\rVert$)\n",
    "while minimizing the proportional drift of the predictions to the wrong side\n",
    "of the margin (i.e., $C \\sum \\xi_i$). Thus, large values of $C$ shunt\n",
    "algorithmic focus towards the correctly classified points near the\n",
    "decision boundary and small values focus on further data. The value $C$ is\n",
    "a hyperparameter for the SVM.\n",
    "\n",
    "The good news is that all of these complicated pieces are handled neatly inside\n",
    "of Scikit-learn. The following sets up the linear *kernel* for the SVM (more on\n",
    "kernels soon),"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.svm import SVC\n",
    "sv = SVC(kernel='linear')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create some synthetic data using `make_blobs` and then\n",
    "fit it to the SVM,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "2"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape='ovr', degree=3, gamma='auto', kernel='linear',\n",
       "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X,y=make_blobs(n_samples=200, centers=2, n_features=2,\n",
    "               random_state=0,cluster_std=.5)\n",
    "sv.fit(X,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After fitting, the SVM now has the estimated support vectors and the\n",
    "coefficients of the $\\boldsymbol{\\beta}$  in the `sv.support_vectors_` and\n",
    "`sv.coef_` attributes, respectively. [Figure](#fig:svm_003) shows the two\n",
    "sample classes (white and gray circles) and the line separating them that was\n",
    "found by the maximal margin algorithm. The two parallel dotted lines show  the\n",
    "margin. The large circles enclose the support vectors, which are the data\n",
    "elements that are relevent to the solution. Notice that only these elements\n",
    "can touch the edges of the margins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
    }
   },
   "outputs": [
    {
     "data": {
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yOAabpmnY7XbEYjFy816O/Px8nDp1Ct988w0sFguAR3H2o0ePorq6mryOYRiMjo6ip6cH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\nkcf8P+Vpb2RaRXOTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0ca69a3c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from matplotlib.pylab import subplots\n",
    "import numpy as np\n",
    "xi = np.linspace(X[:,0].min(),X[:,0].max(),100)\n",
    "\n",
    "fig,ax=subplots()\n",
    "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='o',alpha=.3)\n",
    "_=ax.plot(sv.support_vectors_[:,0],sv.support_vectors_[:,1],'ko',markersize=20,alpha=.2)\n",
    "_=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi- sv.intercept_/sv.coef_[0,1],'k',lw=3.)\n",
    "margin = np.linalg.norm(sv.coef_)\n",
    "_=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi-(sv.intercept_+margin/2.)/sv.coef_[0,1],'--k',lw=3.)\n",
    "_=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi-(sv.intercept_-margin/2.)/sv.coef_[0,1],'--k',lw=3.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/svm_003.png, width=500 frac=0.75]  The\n",
    "two class shown (white and gray circles) are linearly separable. The maximal\n",
    "margin solution is shown by the dark black line in the middle. The dotted lines\n",
    "show the extent of the margin.  The large circles indicate the support vectors\n",
    "for the maximal margin solution. <div id=\"fig:svm_003\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:svm_003\"></div>\n",
    "\n",
    "<p>The two class shown (white and gray circles) are linearly separable. The\n",
    "maximal margin solution is shown by the dark black line in the middle. The\n",
    "dotted lines show the extent of the margin.  The large circles indicate the\n",
    "support vectors for the maximal margin solution.</p>\n",
    "<img src=\"fig-machine_learning/svm_003.png\" width=500>\n",
    "\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "4"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "def draw_margins(sv,X,y,ax=None):\n",
    "    sv.fit(X,y)\n",
    "    xi = np.linspace(X[:,0].min(),X[:,0].max(),100)\n",
    "    if ax is None: fig,ax=subplots()\n",
    "    _=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='o',alpha=.3)\n",
    "    _=ax.plot(sv.support_vectors_[:,0],sv.support_vectors_[:,1],'ko',markersize=20,alpha=.2)\n",
    "    _=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi- sv.intercept_/sv.coef_[0,1],'k',lw=3.)\n",
    "    margin = np.linalg.norm(sv.coef_)\n",
    "    _=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi- (sv.intercept_+margin/2.)/sv.coef_[0,1],'--k',lw=3.)\n",
    "    _=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi- (sv.intercept_-margin/2.)/sv.coef_[0,1],'--k',lw=3.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "5"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mI5lMcv78eZ566im++93v8vnPf57u7m5+/OMfb/qxtqTnHgqFyhaK+P3+srFD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\nm1QqxZEjR3C73fj9flnputoFsJJrvxL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IBAJZX0jBgSu8P8EO7/V6UV1dnaHtz1fKVK/X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\nIlW3UZYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0ca488e2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "X, y = make_blobs(n_samples=50, centers=2, n_features=2,\n",
    "                  cluster_std=1,random_state=0)\n",
    "\n",
    "fig,axs = subplots(2,2,sharex=True,sharey=True)\n",
    "#fig.set_size_inches((12,6))\n",
    "sv = SVC(kernel='linear',C=.0100)\n",
    "draw_margins(sv,X,y,ax=axs[0,0])\n",
    "_=axs[0,0].set_title('C=0.01')\n",
    "sv = SVC(kernel='linear',C=1)\n",
    "draw_margins(sv,X,y,ax=axs[0,1])\n",
    "_=axs[0,1].set_title('C=1')\n",
    "sv = SVC(kernel='linear',C=100)\n",
    "draw_margins(sv,X,y,ax=axs[1,0])\n",
    "_=axs[1,0].set_title('C=100')\n",
    "sv = SVC(kernel='linear',C=10000)\n",
    "draw_margins(sv,X,y,ax=axs[1,1])\n",
    "_=axs[1,1].set_title('C=10000')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Figure](#fig:svm_004) shows what happens when the value of $C$ changes.\n",
    "Increasing this value emphasizes the $\\xi$ part of the objective function in\n",
    "Equation [eq:svm](#eq:svm). As shown in the top left panel, a small value for\n",
    "$C$ means that\n",
    "the algorithm is willing to accept many support vectors at the expense of\n",
    "maximizing the margin. That is, the proportional amount that predictions are on\n",
    "the wrong side of the margin is more acceptable with smaller $C$.  As the value\n",
    "of $C$ increases, there are fewer support vectors because the optimization\n",
    "process prefers to eliminate support vectors that are far away from the margins\n",
    "and accept fewer of these that encroach into the margin. Note that as the value\n",
    "of $C$ progresses through this figure, the separating line tilts slightly.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/svm_004.png, width=500 frac=0.95] The\n",
    "maximal margin algorithm finds the separating line that maximizes the margin\n",
    "shown. The elements that touch the margins are the support elements. The dotted\n",
    "elements are not relevent to the solution. <div id=\"fig:svm_004\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:svm_004\"></div>\n",
    "\n",
    "<p>The maximal margin algorithm finds the separating line that maximizes the\n",
    "margin shown. The elements that touch the margins are the support elements. The\n",
    "dotted elements are not relevent to the solution.</p>\n",
    "<img src=\"fig-machine_learning/svm_004.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "## Kernel Tricks\n",
    "\n",
    "Support Vector Machines provide a powerful method to deal with linear\n",
    "separations, but they can also apply to non-linear boundaries by\n",
    "exploiting the so-called *kernel trick*.  The convex optimization\n",
    "formulation of the SVM includes a *dual* formulation that leads to a\n",
    "solution that requires only the inner-products of the features. The\n",
    "kernel trick is to substitute inner-products by nonlinear kernel\n",
    "functions.  This can be thought of as mapping the original features\n",
    "onto a possibly infinite dimensional space of new features.  That is,\n",
    "if the data are not linearly separable in two-dimensional space (for\n",
    "example) maybe they are separable in three-dimensional space (or\n",
    "higher)?\n",
    "\n",
    "To make this concrete, suppose the original input space is\n",
    "$\\mathbb{R}^n$ and we want to use a non-linear mapping\n",
    "$\\psi:\\mathbf{x} \\mapsto \\mathcal{F}$ where $\\mathcal{F}$ is an\n",
    "inner-product space of higher dimension.  The kernel trick is to\n",
    "calculate the inner-product in $\\mathcal{F}$ using a kernel\n",
    "function, $K(\\mathbf{x}_i,\\mathbf{x}_j) = \\langle\n",
    "\\psi(\\mathbf{x}_i),\\psi(\\mathbf{x}_j)\\rangle$. The long way to\n",
    "compute this is to first compute $\\psi(\\mathbf{x})$ and then do the\n",
    "inner-product. The kernel-trick way to do it is to use the kernel\n",
    "function and avoid computing $\\psi$. In other words, the kernel\n",
    "function returns what the inner-product in $\\mathcal{F}$ would have\n",
    "returned if $\\psi$ had been applied. For example, to achieve an\n",
    "$n^{th}$ polynomial mapping of the input space, we can use\n",
    "$\\kappa(\\mathbf{x}_i,\\mathbf{x}_j)=(\\mathbf{x}_i^T\\mathbf{x}_j+\\theta)^n$.\n",
    "For example, suppose the input space is $\\mathbb{R}^2$ and\n",
    "$\\mathcal{F}=\\mathbb{R}^4$ and we have the following mapping,\n",
    "\n",
    "$$\n",
    "\\psi(\\mathbf{x}) : (x_0,x_1) \\mapsto (x_0^2,x_1^2,x_0 x_1, x_1 x_0)\n",
    "$$\n",
    "\n",
    " The inner product in $\\mathcal{F}$ is then,\n",
    "\n",
    "$$\n",
    "\\langle \\psi(\\mathbf{x}),\\psi(\\mathbf{y})  \\rangle = \\langle\n",
    "\\mathbf{x},\\mathbf{y}  \\rangle^2\n",
    "$$\n",
    "\n",
    " In other words, the kernel is the square of the inner\n",
    "product in input space. The advantage of using the kernel instead of\n",
    "simply enlarging the feature space is computational because you only\n",
    "need to compute the kernel on all distinct pairs of the input space.\n",
    "The following example should help make this concrete. First we create\n",
    "some Sympy variables,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "6"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy as S\n",
    "x0,x1=S.symbols('x:2',real=True)\n",
    "y0,y1=S.symbols('y:2',real=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create the $\\psi$ function that maps into $\\mathbb{R}^4$\n",
    "and the corresponding kernel function,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "7"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psi = lambda x,y: (x**2,y**2,x*y,x*y)\n",
    "kern = lambda x,y: S.Matrix(x).dot(y)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the inner product in $\\mathbb{R}^4$  is\n",
    "equal to the kernel function, which only uses wthe $\\mathbb{R}^2$\n",
    "variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "8"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x0**2*y0**2 + 2*x0*x1*y0*y1 + x1**2*y1**2\n",
      "x0**2*y0**2 + 2*x0*x1*y0*y1 + x1**2*y1**2\n"
     ]
    }
   ],
   "source": [
    "print(S.Matrix(psi(x0,x1)).dot(psi(y0,y1)))\n",
    "print(S.expand(kern((x0,x1),(y0,y1)))) # same as above"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Polynomial Regression Using Kernels.**  Recall our favorite\n",
    "linear regression problem from the regularization chapter,\n",
    "\n",
    "$$\n",
    "\\min_{\\boldsymbol{\\beta}}  \\Vert y - \\mathbf{X}\\boldsymbol{\\beta}\\Vert^2\n",
    "$$\n",
    "\n",
    " where $\\mathbf{X}$ is a $n\\times m$ matrix with $m>n$. As\n",
    "we discussed, there are multiple solutions to this problem. The\n",
    "least-squares solution is the following:\n",
    "\n",
    "$$\n",
    "\\boldsymbol{\\beta}_{LS}=\\mathbf{X}^T(\\mathbf{X}\\mathbf{X}^T)^{\\text{-1}}\\mathbf{\n",
    "y}\n",
    "$$\n",
    "\n",
    " Given a new feature vector $\\mathbf{x}$, the corresponding estimator\n",
    "for $\\mathbf{y}$ is the following,\n",
    "\n",
    "$$\n",
    "\\hat{\\mathbf{y}} = \\mathbf{x}^T\\boldsymbol{\\beta}_{LS}=\\mathbf{x}^T\\mathbf{X}^T(\n",
    "\\mathbf{X}\\mathbf{X}^T)^{\\text{-1}}\\mathbf{y}\n",
    "$$\n",
    "\n",
    " Using the kernel trick, the solution can be written more generally as\n",
    "the following,\n",
    "\n",
    "$$\n",
    "\\hat{\\mathbf{y}}=\\mathbf{k}(\\mathbf{x})^T\\mathbf{K}^{\\text{-1}}\\mathbf{y}\n",
    "$$\n",
    "\n",
    " where the $n\\times n$ kernel matrix $\\mathbf{K}$ replaces\n",
    "$\\mathbf{X}\\mathbf{X}^T$ and where $\\mathbf{k}(\\mathbf{x})$ is a $n$-vector of\n",
    "components $\\mathbf{k}(\\mathbf{x})=[\\kappa(\\mathbf{x}_i,\\mathbf{x})]$ and where\n",
    "$\\mathbf{K}_{i,j}=\\kappa(\\mathbf{x}_i,\\mathbf{x}_j)$ for the kernel function\n",
    "$\\kappa$.  With this more general setup, we can substitute\n",
    "$\\kappa(\\mathbf{x}_i,\\mathbf{x}_j)=(\\mathbf{x}_i^T\\mathbf{x}_j+\\theta)^n$ for\n",
    "$n^{th}$-order polynomial regression [[bauckhagenumpy]](#bauckhagenumpy). Note\n",
    "that ridge\n",
    "regression can also be incorporated by inverting $(\\mathbf{K}+\\alpha\n",
    "\\mathbf{I})$, which can help stabilize poorly conditioned $\\mathbf{K}$ matrices\n",
    "with a tunable $\\alpha$ hyper-parameter [[bauckhagenumpy]](#bauckhagenumpy).\n",
    "\n",
    "For some kernels, the enlarged $\\mathcal{F}$ space is infinite-dimensional.\n",
    "Mercer's conditions provide technical restrictions on the kernel functions.\n",
    "Powerful, well-studied kernels have been implemented in Scikit-learn. The\n",
    "advantage of kernel functions may evaporate for when $n\\rightarrow m$ in which\n",
    "case using the $\\psi$ functions instead can be more practicable.\n",
    "\n",
    "<!-- !bt -->\n",
    "<!-- \\begin{pyconsole} -->\n",
    "<!-- sv = SVC(kernel='rbf',C=1000) -->\n",
    "<!-- sv.fit(X,y) -->\n",
    "<!-- \\end{pyconsole} -->\n",
    "<!-- !et -->\n",
    "\n",
    "<!-- FIGURE: [fig-machine_learning/svm_005.png, width=500 frac=0.85] Using a\n",
    "radial basis function kernel, the SVM can generate a curved separating surface\n",
    "that can classify the two classes shown. <div id=\"fig:svm_005\"></div> -->\n",
    "\n",
    "<!-- As shown in [Figure](#fig:svm_002), the maximal margin algorithm finds the\n",
    "-->\n",
    "<!-- separating line that maximizes the margin shown. As a result, the data\n",
    "shown by -->\n",
    "<!-- the dotted circles are no longer relevant to the *support* of the line.\n",
    "That -->\n",
    "<!-- is, the dotted circles could be removed with changing the final result. -->\n",
    "\n",
    "<!-- Kernel trick -->\n",
    "<!-- objective function includes VC dimension -->\n",
    "\n",
    "<!-- *Modern Multivariate Statistical Techniques Izenman, p. 371* -->\n",
    "<!-- *Learning and Soft computing by Kecman, p.154, 171, 186* -->\n",
    "<!-- *Mastering machine learning with Scikit-learn, p.174* -->\n",
    "<!-- *Gaussian Processes for Machine Learning, p. 163* -->\n",
    "<!-- *Elements of statistical learning p.418* -->\n",
    "<!-- *Kernel methods pattern Taylor p.43* -->\n",
    "<!-- *Learning with Kernels, p.43* -->\n",
    "<!-- *An Intro to Machine Learning by james, p.362* -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "9"
    }
   },
   "outputs": [
    {
     "data": {
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Q0W5Qc7Cr6gSAieW/z4nIEIC9ALZNsHPeDyLaTQztsYtIJ4AXAJw3cr8P28xZ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\nEVkMg52IyGIY7EREFvP/AYGqjdOV+X4OAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0ca2b5b690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pylab import cm\n",
    "xi = np.linspace(X[:,0].min(),X[:,0].max(),100)\n",
    "yi = np.linspace(X[:,1].min(),X[:,1].max(),100)\n",
    "\n",
    "fig,ax=subplots()\n",
    "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='o',alpha=.3)\n",
    "Xi,Yi = np.meshgrid(xi,yi)\n",
    "Zi=sv.predict(np.c_[Xi.ravel(),Yi.ravel()]).reshape(Xi.shape)\n",
    "\n",
    "_=ax.contourf(Xi,Yi,Zi,cmap=cm.Paired,alpha=0.2);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
